A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3#. If side C has a length of #15 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

Question

1187 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-24T12:33:03

side #a=16.0021#
side #b=13.7413#

To solve the triangle use the Sine Law
#a/sin A=b/sin B=c/sin C#

Compute angle B first using the formula #A+B+C=pi#

#B=pi-A-C#

#B=pi-(3pi)/8-pi/3#

#B=(7pi)/24#

Compute side a:

#a/sin A=c/sin C#

#a=(c*sin A)/sin C=15*sin ((3pi)/8)/(sin (pi/3))#

#a=16.0021#

Compute side b:

#b/sin B=c/sin C#

#b=(c*sin B)/sin C=15*sin ((7pi)/24)/(sin (pi/3))#

#b=13.7413#